I just installed Steam and managed to redeem my humble bundle version of Trine 2 on Steam - it works like a charm but how can I move my savefiles/game progress from previous installation to present Steam account? Which files to copy?

It should be possible to do this manually, though I unfortunately can't promise this. If you want to try this, you can move the save files to the Steam's folder for Trine 2 which is the following. I recommend taking a backup copy of the files.

~/.steam/steam/userdata/[ACCOUNT ID]/35720/remote

If you have used only one Steam account on your computer, there is just one user folder but there can be many. Let me know if you need help with figuring out which one is yours.